Seminar by Jonathan Yu-Meng Li

Actuarial Science and Financial Mathematics seminar series 

Jonathan Yu-Meng Li
University of Ottawa

Room: M3 3127

Coherent Wasserstein Transport: A New Approach to Distributionally Robust Optimization

At the heart of Wasserstein distributionally robust optimization (DRO)-an increasingly popular data-driven optimization scheme-is the construction of ambiguity sets via optimal transport. The standard approach defines these sets using the family of type-$p$ Wasserstein metrics (indexed by the power parameter $p \in [1,\infty]$). Although, in principle, higher-order Wasserstein metrics (as $p \rightarrow \infty$) could yield less conservative and more data-driven ambiguity sets, the type-1 Wasserstein metric remains the predominant choice-likely due to its weaker distributional assumptions, greater tractability in DRO formulations, and favorable finite-sample guarantees. Motivated by the potential limitations of higher-order metrics, we introduce new families of transport-based metrics, termed coherent Wasserstein transport, by formulating a risk-averse counterpart of the optimal transport problem using coherent risk measures. Coherent Wasserstein transport achieves flexibility comparable to higher-order metrics for reducing conservatism while inheriting the advantageous properties of the type-1 distance. Specifically, it can accommodate a similar variety of distributions as the type-1 metric, yield DRO problems solvable via convex or linear programs, and enjoy comparable finite-sample guarantees. Extensive computational experiments on overparameterized regression problems demonstrate the practical value of coherent Wasserstein DRO models, which efficiently explores the space between type-1 and type-$\infty$ formulations for enhanced out-of-sample performance. Moreover, these models give rise to novel regularization formulations, presenting a promising avenue for broader applications in data-driven optimization.